Recovery of the Earth’s Gravity Field from GOCE Satellite Gravity Gradiometry: A Case Study

GOCE SGG data were simulated along a 28-day perturbed orbit with an
initial semi-major axis of 6621 km, an inclination of 96.5°, and an
eccentricity of 0.0045. Based on these data, we have estimated
numerically the effects of various (static and time-varying)
geopotential constituents on the components of the gravity gradient
tensor referred to the RTN (radial – quasi-transversal – normal) local
orbit system. We have seen that within the gradiometer’s measurement
bandwidth the recovery of harmonic coefficients may be not affected by
temporal variations of the gravity field. In fact, the total signal of
the sum of considered time-dependent constituents (solid Earth tides up
to degree and order 4, ocean tides up to degree 50 and order 39,
variable atmospheric potential up to degree and order 50) does not
exceed 0.1% of the contribution of the Earth’s static anomalous
potential (GPM98CR gravity model up to degree 720). Even maximal
amplitudes in the spectra of the gravity gradients generated by the sum
of these time-dependent constituents were less than the anticipated
measurement error of the diagonal components of the gravity gradient
tensor. Therefore, in further simulation we take into account only the
Earth’s static potential. The computation of power spectral densities
(PSD) of gravity gradients generated by spherical harmonics of various
degrees has shown that the amplitudes of all harmonics of degree n>250
are less then the anticipated error of GOCE SGG data. Thus, the static
anomalous potential is expected to be recoverable up to degree 250 from
the GOCE gradiometry data processing. In order to de-correlate the
gravity gradients affected by colored noise, several filter approaches
were considered and numerically tested for different sampling rates and
different spectral properties of measurement errors (including white
noise and noise with PSD presumed for GOCE SGG data). As a result, we
come to a simple non-recursive filter technique, which incorporates
observation equations for SGG data within a floating time interval of
fixed length comparable with the GOCE measurement bandwidth. We have
examined this technique for the computation of the filter coefficients
based on (1) the a priori given PSD of noise and (2) a PSD of noise
estimated from the sum of measured diagonal components of the gradient
tensor. Each case gives practically the same results after filtering and
does not change the signal/noise ratio. Naturally, the second case is
closer to real processing of GOCE SGG data. Independently on sampling
rate, no more than 400 data samples are required for a stable
computation of the filter coefficients. We have used the proposed filter
technique for a least-squares estimation of spherical harmonic
coefficients of the Earth’s gravitational potential from 28-day
simulated GOCE SGG data disturbed by colored noise. Finally the results
of recovering spherical harmonic coefficients at various degrees are
discussed.